The image Download button does not appear if the image is a Cover Photo (in the ‘Cover Photos’ album). The Download button appears if the image is not a Cover Photo, even if it’s uploaded by a non-Facebook friend.
The Chrome extension, FB Album Mod or equivalent User/Greasemonkey script for other browsers like Firefox and Opera, will allow you to download the full-resolution version of images in the ‘Cover Photos’ album.
This helps people learn more about you. It also helps us prevent spam, fake profiles, and other content that can detract from your experience on Facebook. An easy way to ensure your cover image is unique is to choose an image from your life, like a photo from a wedding, day at the beach, or birthday party. If you want to use a photo to show solidarity or express support for a cause or organization, you can still post a status or photo.
To add or change your cover photo:
Go to your timeline
Click Add a Cover, or hover over your current cover photo and click Change Cover
Choose whether you want to upload a new photo or pick a photo from one of your existing photo albums
Once you choose a photo, you can reposition it by clicking on the image and dragging it up or down
A cover photo is the larger photo at the top of your timeline, right above your profile picture.
Cover photos are 851 pixels wide and 315 pixels tall. If you upload an image that’s smaller than these dimensions, it will get stretched to this larger size. The image you upload must be at least 399 pixels wide and 150 pixels tall.
To get the fastest load times for your Page, upload an sRGB JPG file that’s 851 pixels wide, 315 pixels tall and less than 100 kilobytes. For images with your logo or text-based content, you may get a higher quality result by using a PNG file.